On the application of KBM method for the 3-D motion of asymmetric rigid body

This article aims to study the three-dimensional motion of a rigid body that rotates about one of its fixed points. The effects of both a Newtonian force field and a moment of a gyrostat are taken into account. In the present work, we have assumed that the body has a spindle initial speed about one of the principal axes of the ellipsoid of inertia. The approximate solutions of the nonlinear problem are obtained by utilizing the Krylov–Bogoliubov–Mitropolski (KBM) technique and its amendments. Such solutions are demonstrated and then illustrated graphically in order to provide an extensive description of the body motion at any time. It is justified that the attained results are in a well consistency with those of the previous works, which are considered as limiting cases. The numerical solutions for governing system of motion are achieved using the fourth-order Runge–Kutta method and represented graphically. The comparison between the analytical solutions and the numerical ones reveals high consistency between them.